Rule 94 -- from Wolfram MathWorld

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Rule 94

Rule 94 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its color and its immediate neighbors. Its rule outcomes are encoded in the binary representation . This rule is illustrated above together with the evolution of a single black cell it produces after 15 steps (Wolfram 2002, p. 55).

Rule 94 is amphichiral, and its complement is 133.

Starting with a single black cell, successive generations , 1, ... are given by interpreting the numbers 1, 7, 27, 119, 427, 1879, 6827, 30039, ... (Sloane's A118101) in binary, namely 1, 111, 11011, 1110111, 110101011, ... (Sloane's A118102). A formula for the the term is given by

$a(n)={1 for n=0; 7 for n=1; 1/6(10+11·4^n) for n>1 odd; 1/3(1+5·4^n) for n>0 even$

(1)

(E. W. Weisstein, Apr. 12, 2006), so computation of rule 94 is computationally reducible for evolution from a single black cell, in which case it has generating function

(2)

Rule 94 is capable of exhibiting nesting and random behavior for some simple initial conditions (Wolfram 2002, p. 951). In particular, the random behavior is most likely to be computationally irreducible.

RELATED WOLFRAM SITES: http://atlas.wolfram.com/01/01/94/

REFERENCES:

Sloane, N. J. A. Sequences A118101 and A118102 in "The On-Line Encyclopedia of Integer Sequences."

Wolfram, S. "Statistical Mechanics of Cellular Automata." Rev. Mod. Phys. 55, 601-644, 1983.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 90, 55, 870, and 952, 2002.

CITE THIS AS:

Weisstein, Eric W. "Rule 94." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Rule94.html